Timeline for Reference for nonlinearity of covers of $\operatorname{SL}(2,\mathbb R)$
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2021 at 22:41 | vote | accept | Jarek Kędra | ||
| Mar 11, 2020 at 19:45 | answer | added | J D | timeline score: 0 | |
| Jul 12, 2016 at 12:43 | comment | added | YCor | It's unclear that this result has a precise author, because I guess that the finite-dimensional representations of the corresponding Lie algebra were classified (middle 19th? Clebsch?) much before the universal covering of $\mathrm{SL}_2(\mathbf{R})$ was defined (no idea where it appeared first!), and the only ingredient of the proof beyond basic Lie theory is this classification of representations of the Lie algebra. | |
| Jul 12, 2016 at 12:38 | history | edited | Jarek Kędra | CC BY-SA 3.0 |
added 131 characters in body
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| Jul 1, 2016 at 7:17 | comment | added | Jarek Kędra | Thank you. Well, of course, it is not so difficult to give a proof. I thought that such a well known (and not obvious) fact should be proven in a textbook. | |
| Jun 29, 2016 at 13:21 | answer | added | Jeffrey Adams | timeline score: 10 | |
| Jun 29, 2016 at 12:12 | comment | added | Sean Lawton | This is addressed here and here. | |
| Jun 29, 2016 at 12:11 | comment | added | Venkataramana | Also see the link: mathoverflow.net/questions/110208/… | |
| Jun 29, 2016 at 12:08 | comment | added | Venkataramana | It is easier to give a proof; every linear representation from the universal cover of $SL_2(\mathbb {R})$ into $GL_n(\mathbb {R})$ yields a complex representation of Lie algebras $\mathfrak {sl}_2(\mathbb {C})$ into $\mathfrak{gl}_n(\mathbb {C})$; since the group $SL_2(\mathbb {C})$ is simply connected, this extends to a holomorphic (algebraic) representation $SL_2(\mathbb {C}) \rightarrow GL_n(\mathbb {C}$; restricting , we get a representation $SL_2(\mathbb{R}\rightarrow GL_n(\mathbb {R})$. Hence the representation can never be faithful on any finite cover of $SL_2(\mathbb{R})$. | |
| Jun 29, 2016 at 11:54 | history | asked | Jarek Kędra | CC BY-SA 3.0 |